Unusual multiple magnetic transitions and anomalous Hall effect observed in antiferromagnetic Weyl semimetal, Mn$_{2.94}$Ge (Ge-rich).

We report on the magnetic and Hall effect measurements of the magnetic Weyl semimetal, Mn$_{2.94}$Ge (Ge-rich) single crystal. From the magnetic properties study, we identify unusual multiple magnetic transitions below the N$\acute{e}$el temperature of 353 K, such as the spin-reorientation ($T_{SR}$) and ferromagnetic-like transitions. Consistent with the magnetic properties, the Hall effect study shows unusual behavior around the spin-reorientation transition. Specifically, the anomalous Hall conductivity (AHC) increases with increasing temperature, reaching a maximum at $T_{SR}$, which then gradually decreases with increasing temperature. This observation is quite in contrast to the Mn$_{3+\delta}$Ge (Mn-rich) system, though both compositions share the same hexagonal crystal symmetry. This study unravels the sensitivity of magnetic and topological properties on the Mn concentration.